Resonating valence-bond physics on the honeycomb lattice

Abstract

We study bond and spin correlations of the nearest-neighbour resonating valence bond (RVB) wavefunction for a SU($2$) symmetric $S=1/2$ antiferromagnet on the honeycomb lattice. We find that spin correlations in this wavefunction are short-ranged, while the bond energy correlation function takes on an oscillatory power-law form $D(\vec{r})\sim \cos (\mathbf{Q}\cdot \vec{r})/|\vec{r}{|}^{{\eta }_w(2)}$, where $\mathbf{Q}=(2\pi /3,-2\pi /3)$ is the wavevector corresponding to "columnar" valence-bond solid order on the honeycomb lattice, and ${\eta }_w(2)\approx 1.49(3)$. We use a recently introduced large-$g$ expansion approach to relate bond-energy correlators of the SU($g$) wavefunction to dimer correlations of an interacting fully-packed dimer model with a three-dimer interaction of strength $V(g)=-\log (1+1/g^2)$. Putting $g=2$, we find numerically that the dimer correlation function $D^d(\vec{r})$ of this dimer model has power-law behaviour $D^d(\vec{r})\sim \cos (\mathbf{Q}\cdot \vec{r})/|\vec{r}{|}^{{\eta }_d(2)}$ with ${\eta }_d(2)\approx 1.520(15)$, in rather good agreement with the wavefunction results. We also study the same quantities for $g=3,4,10$ and find that the bond-energy correlations in the SU($g$) wavefunction are consistently well-reproduced by the corresponding dimer correlations in the interacting dimer model.

10 pages; two-column prb format; 14 .eps figures; v2: version submitted to PRB; v3: published version

References in corpus (7)

• Classical dimers with aligning interactions on the square lattice
• Some formal results for the valence bond basis
• Plaquette valence-bond ordering in J_1-J_2 Heisenberg antiferromagnet on the honeycomb lattice
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• Coexistence of long-range and algebraic correlations for short-range valence-bond wave functions in three dimensions
• Variational RVB wave function for the spin-1/2 Heisenberg Model on honeycomb lattice
• Loop statistics in the toroidal honeycomb dimer model

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• Dulmage-Mendelsohn percolation: Geometry of maximally-packed dimer models and topologically-protected zero modes on site-diluted bipartite lattices
• Indicators of Conformal Field Theory: entanglement entropy and multiple-point correlators
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• Spontaneous layering and power-law order in the three-dimensional fully-packed hard-plate lattice gas
• Flux fractionalization transition in anisotropic $S=1$ antiferromagnets and dimer-loop models